The problem with atomic clocks is that they are affected by gravity, thus the one in Denver and the one in Greenwich run at different rates, (Denver the mile high city, Greenwich at sea level). Also, in 1984 Dr.Van Flandern at the US Naval Observatory noted that the atomic clocks were slowing down relative to orbital time. Since then this has been confirmed by others.
The definition of TAI accounts for the local gravity using Einstein’s theory of General Relativity.
Currently Dynamical Time (the independent argument of the dynamical equations of orbital motion) is defined as TAI + 32.184 seconds. I am unaware of any generally accepted differences between atomic time and graviational (Dynamical) time. There are the intruging issues of the pioneer anomaly and Modified Newtonian Mechanics, but that’s above my pay grade.
So, in a hundred years or so, Greenwich will be under water and only the Denver clock will matter. ;-)